In mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces:...

according to their universal cover. The uniformization theorem is a generalization of the Riemann mapping theorem from proper simply connected open subsets...

onto D {\displaystyle D} . Koebe's uniformization theorem for normal families also generalizes to yield uniformizers f {\displaystyle f} for multiply-connected...

mathematics, the simultaneous uniformization theorem, proved by Bers (1960), states that it is possible to simultaneously uniformize two different Riemann surfaces...

In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with...

studied by Koebe who proved in 1910, as a generalization of the uniformization theorem, that every such surface is conformally equivalent to either the...

Look up uniformization in Wiktionary, the free dictionary. Uniformization may refer to: Uniformization (set theory), a mathematical concept in set theory...

In the context of compact Riemann surfaces X, via the Riemann uniformization theorem, this can be seen as a distinction between the surfaces of different...

geometric proof, which yields a stronger geometric result, is the uniformization theorem. This was originally proven only for Riemann surfaces in the 1880s...

bounded interval has a uniformly convergent subsequence. The main condition is the equicontinuity of the family of functions. The theorem is the basis of many...

theorem Toponogov theorem Sphere theorem Hodge theory Uniformization theorem Yamabe problem Killing vector field Myers-Steenrod theorem Hodge star operator...

structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply connected...

prove a grand uniformization theorem that would establish the new theory more completely. Klein succeeded in formulating such a theorem and in describing...

Lazarus Fuchs. By the uniformization theorem, every Riemann surface is either elliptic, parabolic or hyperbolic. More precisely this theorem states that a Riemann...

infamously known as "Cauchy's wrong theorem". The uniform limit theorem shows that a stronger form of convergence, uniform convergence, is needed to ensure...

Low-dimensional topology is strongly geometric, as reflected in the uniformization theorem in 2 dimensions – every surface admits a constant curvature metric;...

In mathematics, the uniform limit theorem states that the uniform limit of any sequence of continuous functions is continuous. More precisely, let X be...

Low-dimensional topology is strongly geometric, as reflected in the uniformization theorem in 2 dimensions – every surface admits a constant curvature metric;...

In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable...

known proofs of the circle packing theorem. Paul Koebe's original proof is based on his conformal uniformization theorem saying that a finitely connected...

Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as...

homeomorphism. This is a consequence of the uniformization theorem for surfaces and the geometrization theorem for 3-manifolds proved by Perelman. A hyperbolic...

Spherical space form conjecture Thurston elliptization conjecture Uniformization theorem The New Yorker authors explained Perelman's reference to "some ugly...

determines the Riemann surface up to conformal equivalence. By the uniformization theorem, every compact Riemann surface has simply connected universal covering...

Various uniformization theorems can be proved using the equation, including the measurable Riemann mapping theorem and the simultaneous uniformization theorem...

such as the Gauss–Bonnet theorem, the uniformization theorem, the von Mangoldt-Hadamard theorem, and the embeddability theorem. There are other important...

identified with C {\displaystyle \mathbf {C} } . On the other hand, the uniformization theorem, a central result in the classification of Riemann surfaces, states...

In descriptive set theory the Jankov–von Neumann uniformization theorem is a result saying that every measurable relation on a pair of standard Borel spaces...

according to the language of Riemann surfaces. According to the uniformization theorem, every Riemann surface is either elliptic, parabolic or hyperbolic...

whose genus is at least 1 {\displaystyle 1} . The Uniformization theorem and the Gauss–Bonnet theorem can both be applied to orientable Riemann surfaces...